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For the quadratic polynomial f (x) =4x ^...

For the quadratic polynomial `f (x) =4x ^(2)-8ax+a.` the statements (s) which hold good is/are:

A

There is only one integral 'a' gor which f (x) is non- negative `AA x in R`

B

For `a lt 0,` the number zero lies between the zeroes of the polynomial

C

`f (x) =0` has two distinct solutions in `(0,1) ` for `a in ((1)/(7), (4)/(7))`

D

The minimum value of `f (x)` for minimum value of a for which f (x) is non-negative `AA x in R` is 0

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VIKAS GUPTA (BLACK BOOK)-QUADRATIC EQUATIONS -EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. Let x^2-px+q=0, where p in R,q in R have the roots alpha,beta such tha...

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  2. If a,b,c are rational numbers (a gt b gt c gt 0) and quadratic equatio...

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  3. For the quadratic polynomial f (x) =4x ^(2)-8ax+a. the statements (s) ...

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  4. Given a,b, c are three distinct real numbers satisfying the inequality...

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  5. Let f (x) =x ^(2) -4x +c AA x in R, where c is a real constant, then w...

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  6. If 0 lt a lt b lt c and the roots alpha, beta of the equation ax ^(2)...

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  7. If satisfies |x-1| + |x-2|+|x-3|gt6, then :

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  8. If both roots of the quadratic equation ax ^(2)+x+b-a =0 are non real ...

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  9. If a,b are two numbers such that a ^(2) +b^(2) =7 and a ^(3) + b^(3) =...

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  10. The number of non-negative integral ordered pair (s) (x,y) for which ...

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  11. If alpha, beta, gamma and delta are the roots of the equation x ^(4) -...

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  12. The value of 'k' for which roots of the equation 4x^2-2x+k=0 are comp...

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  13. If a,b,c in R, then for which of the following graphs of the quadrati...

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  14. a, b, c, in R, a ne 0 and the quadratic equation ax^(2) + bx + c = 0 h...

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  15. If alpha and beta are the roots of the equation ax ^(2) + bx + c=0,a,b...

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  16. The equation cos ^(2) x - sin x+lamda = 0, x in (0, pi//2) has roots t...

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  17. If the equation ln (x^(2) +5x ) -ln (x+a +3)=0 has exactly one solutio...

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  18. The number of non-negative integral ordered pair (s) (x,y) for which ...

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  19. If a lt 0, then the value of x satisfying x ^(2)-2a|x-a| -3a ^(2)=0 i...

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  20. If 0 lt a lt b lt c and the roots alpha, beta of the equation ax ^(2)...

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